On residual sums of squares in non-parametric autoregression

By relying on the theory of U-statistics of dependent data, the authors have given a detailed analysis of the residual sum of squares, RSS, after fitting a nonlinear autoregression using the kernel method. The asymptotic bias of the RSS as an estimator of the noise variance is evaluated up to and including the first order term. A similar quantity, the cross validated residual sum of squares obtained by ‘leaving one out’ in the fitting is similarly analysed. An asymptotic positive bias is obtained.